'Bracegirdle' is a real English surname, meaning 'trouser-belt'. The first element has several potential sources, but as a Hobbit-name would come from Old English brec 'breech, trouser', with 'girdle' being 'belt'. The punning implication, that members of the family were so rotund as to literally brace their girdles - in the sense that their belts were tightly fastened - is not part of the formal etymology of the name, but would surely not have been lost on the Hobbits, who delighted in jokes like this.

It should be mentioned that some sources suggest and alternative origin via Old French, where the 'brace' element comes from bras, 'arm', and so a 'bracegirdle' would be an archer's leather arm-guard. This Old French etymology is dubious even for the real English surname, and it can surely be discounted entirely as the source of a Hobbit family name.